Vitaly Roman'kov

Vitaly Roman'kov

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular, multiplicative groups of residue rings. We propose two versions of the secret sharing scheme and a version of ($k,n$)-thrested scheme. For a given $n$, the dealer can choose any $k.$ The main feature of the proposed schemes is that the shares of secrets are distributed once and can be used multiple times. This property distinguishes the proposed schemes from the secret sharing schemes known in the literature. The proposed schemes are semantically secure. The same message can be transmitted in different forms. From the transferred secret $c$ it is impossible to determine which of the two given secrets $m_1$ or $m_2$ was transferred. For concreteness, we give some numerical examples.

Vitaly Roman'kov

We show that an attack based on the linear decomposition method introduced by the author can be efficiently applied to the new version of the MOR scheme proposed in \cite{BMSS}. We draw attention to some inaccuracies in the description of this version. We show how the action of an exponent of a given automorphism (for example, the action of its inverse) can be calculated, and we also show how the unknown exponent of automorphism can be calculated if we go over to the corresponding linear transformation. This method can be applied to different matrix groups over an arbitrary constructive field. It does not depend on the specific properties of the underlined matrix group. The considered problem is reduced in probabilistic polynomial time to the similar problem in small extensions of the underlined field.